Analogical Proportions, Multivalued Dependencies and Explanations

Abstract

Analogical proportions are statements of the form “a is to b as c is to d”. They deal simultaneously with the similarities and differences between items, and they may be considered as a building block of analogical inference. This short paper establishes the existence of a close linkage between analogical proportions and (weak) multivalued dependencies in databases, thus providing an unexpected bridge between two distant areas of research: analogical reasoning and database design. (Weak) multivalued dependencies express a form of contextual logical independence. Besides, analogical proportions, which heavily rely on the comparison of items inside pairs and to the pairing of pairs exhibiting identical changes on attributes, are also a tool for providing adverse example-based explanations. Lastly, it is suggested that this may be applied to a data set reporting decisions in order to detect if some decision is unfair with respect to a sensitive variable (fairness being a matter of independence).